CLAT - Mathematical Ability - Surds and Indices

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Question - 1

Which of the following numbers is not equal to -8/27?

  • A \((\frac{2}{3})^{-3}\)
  • B \(-(\frac{2}{3})^{3}\)
  • C \((-\frac{2}{3})^{3}\)
  • D \((\frac{-2}{3})\times(\frac{-2}{3})\times(\frac{-2}{3})\)

Question - 2

\((\frac{-1}{5})^3\div(\frac{-1}{5})^8\) is equal to

  • A \((\frac{-1}{5})^5\)
  • B \((\frac{-1}{5})^{11}\)
  • C (-5)5
  • D \((\frac{1}{5})^5\)

Question - 3

\(\{(\frac{1}{3})^2\}^4\) is equal to

  • A \((\frac{1}{3})^6\)
  • B \((\frac{1}{3})^8\)
  • C \((\frac{1}{3})^{24}\)
  • D \((\frac{1}{3})^{16}\)

Question - 4

\((\frac{2}{3})^{-5}\times(\frac{5}{7})^{-5}\) is equal to

  • A \((\frac{2}{3}\times\frac{5}{7})^{-10}\)
  • B \((\frac{2}{3}\times\frac{5}{7})^{-5}\)
  • C \((\frac{2}{3}\times\frac{5}{7})^{25}\)
  • D \((\frac{2}{3}\times\frac{5}{7})^{-25}\)

Question - 5

Simplify: \((((625)^{-1/2})^{-1/4})^2\)

  • A 0
  • B 5
  • C 3
  • D 4

Question - 6

Evaluate: \((\frac{16}{81})^{3/4}\times(\frac{16}{81})^{-5/4}\)

  • A \(\frac{256}{6561}\)
  • B 0
  • C \(-\frac{256}{6561}\)
  • D \(+\frac{256}{6561}\)

Question - 7

Evaluate: \((\frac{16}{81})^{5/4}\div(\frac{16}{81})^{3/4}\)

  • A \(-\frac{4}{9}\)
  • B \(\frac{9}{4}\)
  • C \(-\frac{9}{4}\)
  • D \(\frac{4}{9}\)

Question - 8

Simplify: \((\frac{x^a}{x^b})^{\frac{1}{ab}}.(\frac{x^b}{x^c})^{\frac{1}{bc}}.(\frac{x^c}{x^a})^{\frac{1}{ca}}\)

  • A 1
  • B 0
  • C 2
  • D 3

Question - 9

84.2 x 642.1x 78.4 x 563.5 = (56)?

  • A 9.8
  • B 11.9
  • C 12.6
  • D 18.2

Question - 10

If \((\frac{a}{b})^{x-1}=(\frac{b}{a})^{x-3}\), then x=?

  • A \(\frac{1}{2}\)
  • B 1
  • C 2
  • D \(\frac{7}{2}\)